AQ 232 – Fish Population Dynamics and Stock Assessment

2. Acoustic Surveys

• The hydroacoustic survey uses an echo sounder to conduct acoustic biomass estimation.
• It is widely used for assessing pelagic fish stocks (e.g., sardines, anchovies, herring, mackerel, tuna).

2. Acoustic Surveys

• In practice for fish stock assessment, acoustic surveys are used to estimate fish stock.
• These surveys are used to estimate the abundance of fish species that form schools in the water column.
• They are particularly useful for pelagic species that are difficult to sample with traditional trawl surveys.

Acoustic Surveys: Key Terms

• Acoustic survey - A survey that uses acoustic sound to estimate fish stock.
• Echo sounder - A device that uses sound waves to detect fish.
• Echo - A sound wave that is reflected back to the sounder.
• Hydroacoustic survey - A survey that uses hydroacoustic sound to estimate fish stock.
• Hydroacoustic means using sound in water.

Acoustic survey methodology

• An acoustic transducer emits a brief, focused pulse of sound into the water.
• If the sound encounters objects that are of different density than the surrounding medium, such as fish, they reflect some sound back toward the source.
• The time it takes for the echo to return is used to calculate the distance to the object.

Acoustic survey methodology…

• These echoes provide information on fish size, location, and abundance.
• The basic components of the scientific echo sounder hardware function is to transmit the sound, receive, filter and amplify, record, and analyze the echoes.
• While there are many manufacturers of commercially available fish-finders, quantitative analysis requires that measurements be made with calibrated echo sounder equipment, having high signal-to-noise ratios.

Principle of echo sounding

• Everything scattered in the water column reflects sound waves depending on the frequency of the waves.
• The higher frequency the shorter the wave length.
• Therefore frequencies > 200 KHz can produce echo from plankton.
• For fishes, a lower frequency < 200 KHz is used

Conditions for echo sounding

• Suitable for small pelagic fish stocks (big pelagic fishes eg. Tuna swim very fast and therefore the method becomes unsuitable).

• The behavior of the fish to be assessed must be known

  • e.g the distribution of the fish in the water column at different times
  • The reaction of the fish towards the fishing boat should also be taken into account.

• The use of a smaller boat towed by the bigger vessel to carry the transducer helps to detect fish which are frightened by the vessel.

Limitations of echo sounders

• Sound beam interference by sound scatters eg. temperature stratification, air bubbles, sediments, debris, vegetation

• Unsuitable for very shallow depths because of the blind zone that exists a few meters below the transducer depending on the diameter of the transducer and the frequency of the sound waves.

  • The larger the diameter the larger the zone.
  • Very deep waters calls for a stronger pulse generating echo sounder

3. Underwater Visual Census Survey (UVCS)

• The more traditional method in which diver count fish along transects
• It involves an observer, equipped with SCUBA gear, estimating the abundance of fish within a given area (the belt transect).
• A multitude of factors, including fish mobility and habitat complexity, have been shown to effect the precision of the counting technique.

Applications of UVCS

- Reef fish communities
- Shallow coastal waters
- Clear water environments
- Surface schooling species (tuna, sardines)

Underwater Methods

Advantages & disadvantages of UVCS

4. Catch per unit effort (CPUE)

• CPUE is catch obtained per standardized unit of fishing effort
• Used as an index of abundance (relative, not absolute)
• Catch rate (CPUE) is frequently and single most useful index for long-term monitoring of a fishery

4. Catch per unit effort (CPUE)…

Formula:

\[\text{CPUE} = \frac{\text{Total Catch}}{\text{Total Effort}}\]

Effort units:

• Fishing hours or days at sea
• Number of hooks (longline)
• Number of fishers
• Number of vessels
• Number of gears

4. Catch per unit effort (CPUE)…

• Changes in CPUE may give an indication of what is happening to the fish stock size
• In theory, a constant trend of CPUE values represents a stable stock
• A rising trend indicates an increasing stock
• Increases in CPUE may mean that a fish stock is recovering and more fishing effort can be applied.

4. Catch per unit effort (CPUE)…

• A falling trend signifies a declining stock

• A declines in CPUE may mean that the fish population cannot support the level of harvesting.

• However, a falling trend does not necessarily indicate overfishing;

  • A fish stock will always decline from its initial high level when fishing occurs until it reaches an equilibrium level, when productivity balances the catch being taken.

• CPUE can therefore be used as an index of stock abundance

Advantages & disadvantages of CPUE

Advantages:

• Uses existing commercial data
• Cost-effective
• Long time series available in many areas
• Large spatial coverage
• Real-time updates possible

Advantages & disadvantages of CPUE

Disadvantages:

• Differences regarding interpretation of fishing effort

• Changes in actual or effective effort as a result of technological development

• Also influenced by skills, experience

• Affected by fisher behavior

• May not reflect true abundance

• Reporting biases

• It is also difficult to know what factors of the fishing operations are important to measure

• It is difficult to keep up with fishery changes

  eg. CPUE could be altered without it being reflected on the stock size

  • A boat may install a more powerful motor
    
  • Or change from day to night fishing.

• Not useful for measuring changes in the stock size of schooling fish species

  • eg. a pelagic species which schools at the surface can be easily seen from fishing boats or spotter planes therefore can be caught in bulk by purse seine nets.

5. Mark-Recapture Methods

• Is a Relative Fish abundance estimation
• It involves capturing, marking, release and recapturing
• The basic concept is that;
  • The ratio of recaptures in the second sample is equivalent to the proportion of those that were marked during the first sampling occasion to the whole population.

5. Mark-Recapture Methods…

• Then, estimation of population size (N) will be;

\[ \frac{m_2}{n_2} = \frac{n_1}{N} \]

• Sample 1 – marked and released

  • \(n_1\) = number captured and marked on the 1st sampling occasion

• Sample 2 - number of recaptures recorded

  • \(n_2\) = number captured on the second sampling occasion
  • \(m_2\) = number of recaptures on the second occasion

Assumptions for mark recapture method

• The population is closed so that N remains constant

  • i.e. there is no movement in or out by birth, death, immigration or recruitment

• All the fish have the same probability of being caught

• Marked and unmarked fish have equal capture probability

• The second sample is a random sample of the population

• No marks of fish are lost between the sampling occasions

• No marks go unrecorded during the second sampling

• Marks do not affect survival

Advantages & disadvantages of Mark-Recapture

Mark-Recapture: Example 1

Problem:

500 tilapia are captured, marked, and released in Lake Victoria. One week later, 200 fish are recaptured, of these, 25 have marks. Find the population estimate in the lake.

Solution

Using the mark-recapture formula:

\[\frac{m_2}{n_2} = \frac{n_1}{N}\]

Where:

• \(n_1 = 500\) (marked fish released)
• \(n_2 = 200\) (fish recaptured)
• \(m_2 = 25\) (marked fish recaptured)
• \(N\) = ??? (unknown population size)

Rearranging the formula to solve for \(N\): \[N = \frac{n_1 \times n_2}{m_2}\] Substituting the values: \[N = \frac{500 \times 200}{25} = 4000\]

The estimated population size of tilapia in Lake Victoria is 4000 fishes.

Mark-Recapture: Example 2

In a capture-recapture process, 200 fishes were tagged. From the capture results, the game warden estimates that, the lake contains 2500 fishes. What percentage of fishes were tagged?

Solution

Let p be the percent of tagged fishes;

\[ \frac{n_1}{N} = \frac{p}{100} \]

\(\frac{200}{2500}=\frac{p}{100}\)

\(p = 8\%\)

• About \(8\%\) of fishes were tagged

6. Depletion Methods

• This method is mainly used for shell fish fishery i.e Octopus
• The method uses either of the two models i.e Leslie and DeLury methods which depend upon the following assumptions;
• Fishing (or sampling) must take a significant proportion of the population causing a depletion

6. Depletion method…

• The decrease in catch per unit effort is proportional to;

  • The reduction in the population
    
  • Catchability of fish remains constant
    
  • Units of effort (or fishing gear) do not compete with one another - remains the same
    
  • The entire population is available to the fishery
    
  • There is no recruitment, natural mortality, immigration or emigration in the population.

6. Depletion method…

• It involves the removal of individuals from a stock and measuring the resulting decrease in relative abundance using CPUE as an abundance index.
• It involves fishing on a closed population in which there is no immigration and emigration
• Time interval is short enough to ignore losses due to natural mortality.

6. Depletion method…

Leslie Method:

\[ \frac{C_t}{f_t} = q(N_o - IC) \qquad(1)\]

Where;

• \(C_t\) = number of fish caught at time t
• \(f_t\) = effort expended in taking \(C_t\)
• \(\frac{C_t}{f_t}\) = catch per unit effort at time t (CPUE)
• \(N_o\) = initial population size
• \(q\) = catchability
• \(IC\) = accumulated catch

6. Depletion method…

Or the Leslie formula can be expressed as;

\[ C_t = qN_0 - q\sum_{i=1}^{t-1}C_i \qquad(2)\]

Where:

• \(C_t\) = Catch in period \(t\)

• \(q\) = Catchability coefficient

• \(N_0\) = Initial population size

• \(\sum_{i=1}^{t-1}C_i\) = Cumulative catch up to time \(t-1\)

• Then, plot \(C_t\) vs. cumulative catch; y-intercept = \(qN_0\), slope = \(-q\)

Leslie Method: Octopus Example

# Octopus depletion study data (Tanzanian coastal fishery)
octopus_data <- tibble(
  period = 1:10,
  effort = c(50, 55, 60, 65, 70, 75, 80, 85, 90, 95),
  days = rep(5, times = 10),
  catch = c(585, 552, 517, 483, 448, 412, 375, 338, 299, 258),
  cumulative_catch = cumsum(catch),
  cpue = catch / (effort * days)
)

# **Results:**

# - **Initial Population ($N_0$):** ~8,267 octopus
# - **Catchability ($q$):** 0.0138
# - **Total Depletion:** 4,267 individuals (52% of stock)

Leslie Data Table

Leslie Method: Octopus Example…

# Fit linear regression: Catch vs Cumulative Catch
leslie_model <- lm(catch ~ cumulative_catch, data = octopus_data)
N0_estimate <- coef(leslie_model)[1]
q_estimate <- -coef(leslie_model)[2]

# intercept = coef(leslie_model)[1]
# q = coef(leslie_model)[2] #slope
# from C_t = qN0 - q*IC
# intercept = qN0
# therefore N0 = intercept/q

Leslie graph

Advantages & disadvantages of depletion methods

7. Pelagic Egg and Larval Surveys

Principle:

• Sample ichthyoplankton (fish eggs and larvae)
• Estimate spawning stock biomass from egg production

7. Pelagic Egg and Larval Surveys..

Daily Egg Production Method (DEPM):

\[SSB = \frac{P_0 \times A}{R \times S \times F}\]

Where:

• \(SSB\) = Spawning stock biomass
• \(P_0\) = Daily egg production per unit area
• \(A\) = Spawning area
• \(R\) = Sex ratio (proportion female)
• \(S\) = Spawning fraction (proportion spawning per day)
• \(F\) = Batch fecundity (eggs per spawning female)

Parameter interpretation

\(P_0\) (Daily Egg Production): Measures spawning intensity in the survey area. Higher \(P_0\) indicates active spawning; reflects reproductive output per unit spawning habitat.

\(A\) (Spawning Area): Geographic extent of the spawning ground. Larger area = greater total egg production. Accurate delineation is critical.

\(R\) (Sex Ratio): Only females produce eggs. Must adjust for proportion of females in spawning population.

\(S\) (Spawning Fraction): Not all females spawn on a given day. Varies by species and environmental conditions. Lower \(S\) = smaller daily fraction of stock spawning.

\(F\) (Batch Fecundity): Individual female reproductive capacity. Higher \(F\) = fewer females needed to produce observed eggs. Critical parameter often determined from histological analysis.

Sample question 1:

A sardine spawning survey in Tanzanian coastal waters collected the following data:

• Daily egg production per unit area (\(P_0\)) = 450 eggs/m²/day
• Spawning area (\(A\)) = 5,000 km²
• Sex ratio (\(R\)) = 0.52 (52% female)
• Spawning fraction (\(S\)) = 0.35 (35% spawn per day)
• Batch fecundity (\(F\)) = 12,000 eggs/female

Calculate the spawning stock biomass (SSB) of sardine given that each sardine egg weighs ~0.75 mg.

Answer:

First, convert spawning area to m²: \[A = 5,000 \text{ km}^2 = 5,000 \times 10^6 \text{ m}^2 = 5 \times 10^9 \text{ m}^2\]

Apply DEPM formula: \[SSB = \frac{450 \times 5 \times 10^9}{0.52 \times 0.35 \times 12,000}\]

\[SSB = \frac{2.25 \times 10^{12}}{2,184} = 1.03 \times 10^9 \text{ eggs}\]

Converting to biomass (sardine eggs ~0.75 mg = 0.00075 g per egg): \[1.03 \times 10^9 \text{ eggs} \times 0.00075 \text{ g/egg} = 7.73 \times 10^8 \text{ g}\]

Convert to tonnes (1 tonne = \(10^6\) g): \[\frac{7.73 \times 10^8 \text{ g}}{10^6 \text{ g/tonne}} = 773 \text{ tonnes}\]

\[SSB \approx 773 \text{ tonnes}\]

Applications Egg/Larval Surveys

Best suited for:

• Species with pelagic eggs (sardines, anchovies, cod)
• Spawning aggregations
• When adult surveys are difficult

Requirements:

• Knowledge of spawning season and area
• Fecundity estimates
• Egg development rates (temperature-dependent)
• Egg mortality rates

Summary

• No single method is perfect for all situations
• Direct methods (surveys) provide independent estimates but are costly
• Indirect methods (CPUE, depletion) use existing data but have biases
• Statistical models integrate multiple sources for best estimates
• Choice depends on species, data, resources, and management needs
• Multiple methods increase confidence in abundance estimates

Last updated: February 2026